A circular coil of radius $$R = 0.10\,\text{m}$$, $$N = 100$$ turns, $$I = 2\,\text{A}$$ has its axis horizontal. At the centre, $$B = 4\pi\times10^{-4}\,\text{T}$$. At $$x = R$$ on the axis, $$B$$ is:

A proton enters a magnetic field $$B = 0.5\,\text{T}$$ at $$v = 4\times10^6\,\text{m/s}$$ at $$\theta = 60°$$ to $$B$$. The pitch of the helical path is: ($$m_p = 1.67\times10^{-27}\,\text{kg}$$)

**Assertion (A):** An ideal ammeter has zero resistance. **Reason (R):** A zero-resistance ammeter does not alter the current in the circuit being measured.

A galvanometer of resistance $$G = 100\,\Omega$$ has a shunt of $$S = 1\,\Omega$$ connected. What fraction of the total current flows through the galvanometer?

**Assertion (A):** The magnetic field due to a finite straight wire is given by $$B = (\mu_0 I/4\pi d)(\sin\alpha + \sin\beta)$$. **Reason (R):** This formula is derived using the superposition principle from the Biot-Savart law.